The asymptotic distribution of a cluster-index for i.i.d. normal random variables

Details The asymptotic distribution of a cluster-index for i.i.d. normal random variables The asymptotic distribution of a cluster-index for i.i.d. normal random variables

2009-06-12

arxiv.org/abs/0906.2334v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 585-595

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP553 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP553

In a sample variance decomposition, with components functions of the sample's
spacings, the largest component $\tilde{I}_n$ is used in cluster detection. It
is shown for normal samples that the asymptotic distribution of $\tilde{I}_n$
is the Gumbel distribution.

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